【数据结构】AVL Tree 二叉平衡树

数据结构源码

实现类


import java.util.ArrayList;
public class AVLTree<K extends Comparable<K>, V> {
    private class Node{
        public K key;
        public V value;
        public Node left, right;
        public int height;
        public Node(K key, V value){
            this.key = key;
            this.value = value;
            left = null;
            right = null;
            height = 1;
        }
    }
    private Node root;
    private int size;
    public AVLTree(){
        root = null;
        size = 0;
    }
    public int getSize(){
        return size;
    }
    public boolean isEmpty(){
        return size == 0;
    }
    // 判别二叉树是否是一颗二分搜索树
    public boolean isBST() {
        ArrayList<K> keys = new ArrayList<>();
        inOrder(root, keys);
        for (int i = 1; i < keys.size(); i++) {
            if (keys.get(i - 1).compareTo(keys.get(i)) > 0) {
                return false;
            }
        }
        return true;
    }
    private void inOrder(Node node, ArrayList<K> keys) {
        if (node == null)
            return;
        inOrder(node.left, keys);
        keys.add(node.key);
        inOrder(node.right, keys);
    }
    // 判别二叉树是否是一颗平衡二叉树
    public boolean isBalanced() {
        return isBalanced(root);
    }
    // 判别以Node为根的二叉树是否是一颗平衡二叉树，递归算法
    private boolean isBalanced(Node node) {
        if (node == null) {
            return true;
        }
        int balanceFactor = getBalanceFactor(node);
        if (Math.abs(balanceFactor) > 1) {
            return false;
        }
        return isBalanced(node.left) && isBalanced(node.right);
    }
    private int getHeight(Node node) {
        if (node == null) {
            return 0;
        }
        return node.height;
    }
    // 取得结点node的平衡因子
    private int getBalanceFactor(Node node) {
        if (node == null)
            return 0;
        return getHeight(node.left) - getHeight(node.right);
    }
    /**
     * 对结点y进行向右旋转，回来旋转之后新的根结点x
     *            y                                      x
     *           / \                                    / \
     *          x   T4          向右旋转                z    y
     *         /     \       - - - - - - - - ->      / \   / \
     *        z      T3                            T1  T2 T3  T4
     *       / \
     *      T1 T2
     *
     * @param y
     * @return
     */
    private Node rightRotate(Node y) {
        Node x = y.left;
        Node T3 = x.right;
        // 向右旋转进程
        x.right = y;
        y.left = T3;
        // 更新height
        y.height = Math.max(getHeight(y.left), getHeight(y.right)) + 1;
        x.height = Math.max(getHeight(x.left), getHeight(x.right)) + 1;
        return x;
    }
    /**
     * 对结点y进行向左旋转操作，回来旋转后的新根结点x
     *        y                                    x
     *      /  \                                 /  \
     *    T1    x            向左旋转 (y)        y     z
     *        /  \        - - - - - - - - ->  / \   /  \
     *       T2   z                          T1 T2 T3  T4
     *          /  \
     *         T3  T4
     * @param y
     * @return
     */
    private Node leftRotate(Node y) {
        Node x = y.right;
        Node T2 = x.left;
        // 向左旋转进程
        x.left = y;
        y.right = T2;
        // 更新height
        y.height = Math.max(getHeight(y.left), getHeight(y.right)) + 1;
        x.height = Math.max(getHeight(x.left), getHeight(x.right)) + 1;
        return x;
    }
    // 向AVL中增加新的元素(key, value)
    public void add(K key, V value){
        root = add(root, key, value);
    }
    // 向以node为根的AVL中刺进元素(key, value)，递归算法
    // 回来刺进新节点后AVL的根
    private Node add(Node node, K key, V value){
        if(node == null){
            size ++;
            return new Node(key, value);
        }
        if(key.compareTo(node.key) < 0)
            node.left = add(node.left, key, value);
        else if(key.compareTo(node.key) > 0)
            node.right = add(node.right, key, value);
        else // key.compareTo(node.key) == 0
            node.value = value;
        // 更新height
        node.height = 1 + Math.max(getHeight(node.left), getHeight(node.right));
        // 核算平衡因子
        int balanceFactor = getBalanceFactor(node);
        // 平衡保护
        if (balanceFactor > 1 && getBalanceFactor(node.left) >= 0) {
            return rightRotate(node);
        }
        if (balanceFactor < -1 && getBalanceFactor(node.right) <= 0) {
            return leftRotate(node);
        }
        if (balanceFactor > 1 && getBalanceFactor(node.left) < 0) {
            node.left = leftRotate(node.left);
            return rightRotate(node);
        }
        if (balanceFactor < -1 && getBalanceFactor(node.right) > 0) {
            node.right = rightRotate(node.right);
            return leftRotate(node);
        }
        return node;
    }
    // 回来以node为根节点的AVL中，key地点的节点
    private Node getNode(Node node, K key){
        if(node == null)
            return null;
        if(key.equals(node.key))
            return node;
        else if(key.compareTo(node.key) < 0)
            return getNode(node.left, key);
        else // if(key.compareTo(node.key) > 0)
            return getNode(node.right, key);
    }
    public boolean contains(K key){
        return getNode(root, key) != null;
    }
    public V get(K key){
        Node node = getNode(root, key);
        return node == null ? null : node.value;
    }
    public void set(K key, V newValue){
        Node node = getNode(root, key);
        if(node == null)
            throw new IllegalArgumentException(key + " doesn't exist!");
        node.value = newValue;
    }
    // 回来以node为根的AVL的最小值地点的节点
    private Node minimum(Node node){
        if(node.left == null)
            return node;
        return minimum(node.left);
    }
    // 从AVL中删去键为key的节点
    public V remove(K key){
        Node node = getNode(root, key);
        if(node != null){
            root = remove(root, key);
            return node.value;
        }
        return null;
    }
    private Node remove(Node node, K key){
        if( node == null )
            return null;
        Node retNode;
        if(key.compareTo(node.key) < 0){
            node.left = remove(node.left, key);
            retNode = node;
        }
        else if(key.compareTo(node.key) > 0){
            node.right = remove(node.right, key);
            retNode = node;
        }
        else{   // key.compareTo(node.key) == 0
            // 待删去节点左子树为空的状况
            if(node.left == null){
                Node rightNode = node.right;
                node.right = null;
                size --;
                retNode = rightNode;
            }
            else if(node.right == null){  // 待删去节点右子树为空的状况
                Node leftNode = node.left;
                node.left = null;
                size --;
                retNode = leftNode;
            }
            else {
                // 待删去节点左右子树均不为空的状况
                // 找到比待删去节点大的最小节点, 即待删去节点右子树的最小节点
                // 用这个节点代替待删去节点的方位
                Node successor = minimum(node.right);
                successor.right = remove(node.right, successor.key);
                successor.left = node.left;
                node.left = node.right = null;
                retNode = successor;
            }
        }
        if (retNode == null)
            return null;
        // 更新height
        retNode.height = 1 + Math.max(getHeight(node.left), getHeight(node.right));
        // 核算平衡因子
        int balanceFactor = getBalanceFactor(retNode);
        // 平衡保护
        if (balanceFactor > 1 && getBalanceFactor(retNode.left) >= 0) {
            return rightRotate(retNode);
        }
        if (balanceFactor < -1 && getBalanceFactor(retNode.right) <= 0) {
            return leftRotate(retNode);
        }
        if (balanceFactor > 1 && getBalanceFactor(retNode.left) < 0) {
            retNode.left = leftRotate(retNode.left);
            return rightRotate(retNode);
        }
        if (balanceFactor < -1 && getBalanceFactor(retNode.right) > 0) {
            retNode.right = rightRotate(retNode.right);
            return leftRotate(retNode);
        }
        return retNode;
    }
    public static void main(String[] args){
    }
}

数据结构拆解

保护字段和内部类


    private class Node{
        public K key;
        public V value;
        public Node left, right;
        public int height;
        public Node(K key, V value){
            this.key = key;
            this.value = value;
            left = null;
            right = null;
            height = 1;
        }
    }
    private Node root;
    private int size;

结构函数

    public AVLTree(){
        root = null;
        size = 0;
    }

增


    // 向AVL中增加新的元素(key, value)
    public void add(K key, V value){
        root = add(root, key, value);
    }
    // 向以node为根的AVL中刺进元素(key, value)，递归算法
    // 回来刺进新节点后AVL的根
    private Node add(Node node, K key, V value){
        if(node == null){
            size ++;
            return new Node(key, value);
        }
        if(key.compareTo(node.key) < 0)
            node.left = add(node.left, key, value);
        else if(key.compareTo(node.key) > 0)
            node.right = add(node.right, key, value);
        else // key.compareTo(node.key) == 0
            node.value = value;
        // 更新height
        node.height = 1 + Math.max(getHeight(node.left), getHeight(node.right));
        // 核算平衡因子
        int balanceFactor = getBalanceFactor(node);
        // 平衡保护
        if (balanceFactor > 1 && getBalanceFactor(node.left) >= 0) {
            return rightRotate(node);
        }
        if (balanceFactor < -1 && getBalanceFactor(node.right) <= 0) {
            return leftRotate(node);
        }
        if (balanceFactor > 1 && getBalanceFactor(node.left) < 0) {
            node.left = leftRotate(node.left);
            return rightRotate(node);
        }
        if (balanceFactor < -1 && getBalanceFactor(node.right) > 0) {
            node.right = rightRotate(node.right);
            return leftRotate(node);
        }
        return node;
    }

删


    // 从AVL中删去键为key的节点
    public V remove(K key){
        Node node = getNode(root, key);
        if(node != null){
            root = remove(root, key);
            return node.value;
        }
        return null;
    }
    private Node remove(Node node, K key){
        if( node == null )
            return null;
        Node retNode;
        if(key.compareTo(node.key) < 0){
            node.left = remove(node.left, key);
            retNode = node;
        }
        else if(key.compareTo(node.key) > 0){
            node.right = remove(node.right, key);
            retNode = node;
        }
        else{   // key.compareTo(node.key) == 0
            // 待删去节点左子树为空的状况
            if(node.left == null){
                Node rightNode = node.right;
                node.right = null;
                size --;
                retNode = rightNode;
            }
            else if(node.right == null){  // 待删去节点右子树为空的状况
                Node leftNode = node.left;
                node.left = null;
                size --;
                retNode = leftNode;
            }
            else {
                // 待删去节点左右子树均不为空的状况
                // 找到比待删去节点大的最小节点, 即待删去节点右子树的最小节点
                // 用这个节点代替待删去节点的方位
                Node successor = minimum(node.right);
                successor.right = remove(node.right, successor.key);
                successor.left = node.left;
                node.left = node.right = null;
                retNode = successor;
            }
        }
        if (retNode == null)
            return null;
        // 更新height
        retNode.height = 1 + Math.max(getHeight(node.left), getHeight(node.right));
        // 核算平衡因子
        int balanceFactor = getBalanceFactor(retNode);
        // 平衡保护
        if (balanceFactor > 1 && getBalanceFactor(retNode.left) >= 0) {
            return rightRotate(retNode);
        }
        if (balanceFactor < -1 && getBalanceFactor(retNode.right) <= 0) {
            return leftRotate(retNode);
        }
        if (balanceFactor > 1 && getBalanceFactor(retNode.left) < 0) {
            retNode.left = leftRotate(retNode.left);
            return rightRotate(retNode);
        }
        if (balanceFactor < -1 && getBalanceFactor(retNode.right) > 0) {
            retNode.right = rightRotate(retNode.right);
            return leftRotate(retNode);
        }
        return retNode;
    }

改


    /**
     * 对结点y进行向右旋转，回来旋转之后新的根结点x
     *            y                                      x
     *           / \                                    / \
     *          x   T4          向右旋转                z    y
     *         /     \       - - - - - - - - ->      / \   / \
     *        z      T3                            T1  T2 T3  T4
     *       / \
     *      T1 T2
     *
     * @param y
     * @return
     */
    private Node rightRotate(Node y) {
        Node x = y.left;
        Node T3 = x.right;
        // 向右旋转进程
        x.right = y;
        y.left = T3;
        // 更新height
        y.height = Math.max(getHeight(y.left), getHeight(y.right)) + 1;
        x.height = Math.max(getHeight(x.left), getHeight(x.right)) + 1;
        return x;
    }
    /**
     * 对结点y进行向左旋转操作，回来旋转后的新根结点x
     *        y                                    x
     *      /  \                                 /  \
     *    T1    x            向左旋转 (y)        y     z
     *        /  \        - - - - - - - - ->  / \   /  \
     *       T2   z                          T1 T2 T3  T4
     *          /  \
     *         T3  T4
     * @param y
     * @return
     */
    private Node leftRotate(Node y) {
        Node x = y.right;
        Node T2 = x.left;
        // 向左旋转进程
        x.left = y;
        y.right = T2;
        // 更新height
        y.height = Math.max(getHeight(y.left), getHeight(y.right)) + 1;
        x.height = Math.max(getHeight(x.left), getHeight(x.right)) + 1;
        return x;
    }


    public void set(K key, V newValue){
        Node node = getNode(root, key);
        if(node == null)
            throw new IllegalArgumentException(key + " doesn't exist!");
        node.value = newValue;
    }

查


    public int getSize(){
        return size;
    }
    public boolean isEmpty(){
        return size == 0;
    }
    // 判别二叉树是否是一颗二分搜索树
    public boolean isBST() {
        ArrayList<K> keys = new ArrayList<>();
        inOrder(root, keys);
        for (int i = 1; i < keys.size(); i++) {
            if (keys.get(i - 1).compareTo(keys.get(i)) > 0) {
                return false;
            }
        }
        return true;
    }
    private void inOrder(Node node, ArrayList<K> keys) {
        if (node == null)
            return;
        inOrder(node.left, keys);
        keys.add(node.key);
        inOrder(node.right, keys);
    }
    // 判别二叉树是否是一颗平衡二叉树
    public boolean isBalanced() {
        return isBalanced(root);
    }
    // 判别以Node为根的二叉树是否是一颗平衡二叉树，递归算法
    private boolean isBalanced(Node node) {
        if (node == null) {
            return true;
        }
        int balanceFactor = getBalanceFactor(node);
        if (Math.abs(balanceFactor) > 1) {
            return false;
        }
        return isBalanced(node.left) && isBalanced(node.right);
    }


    private int getHeight(Node node) {
        if (node == null) {
            return 0;
        }
        return node.height;
    }
    // 取得结点node的平衡因子
    private int getBalanceFactor(Node node) {
        if (node == null)
            return 0;
        return getHeight(node.left) - getHeight(node.right);
    }


    // 回来以node为根节点的AVL中，key地点的节点
    private Node getNode(Node node, K key){
        if(node == null)
            return null;
        if(key.equals(node.key))
            return node;
        else if(key.compareTo(node.key) < 0)
            return getNode(node.left, key);
        else // if(key.compareTo(node.key) > 0)
            return getNode(node.right, key);
    }
    public boolean contains(K key){
        return getNode(root, key) != null;
    }
    public V get(K key){
        Node node = getNode(root, key);
        return node == null ? null : node.value;
    }
    // 回来以node为根的AVL的最小值地点的节点
    private Node minimum(Node node){
        if(node.left == null)
            return node;
        return minimum(node.left);
    }